@RCAFDM Love your blog. I have an idea for the focus of your next analysis. Is there some way I can contact you privately?
Why don't you just simulate some data? The exact results depends on the causal paths, existence of other causes and their gaps , measurement error in the predictor, see e.g. http://emilkirkegaard.dk/understanding_statistics/?app=test_bias_omitted_variable_bias …
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Actually, I just simulated it and published it on RPubs. It's not measurement error btw. http://rpubs.com/random_critical_analysis/inverse_confusion_with_continuous_variables …
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I was thinking this would have been better described by someone else previously, but I think this gets the point across OK (especially in this particular context)
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I've seen this with inverting real-life datasets of this sort, so I'm particularly attuned to it. It makes sense if you think about it, but it's an easy mistake to make.
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Note: I'm not suggesting measurement error, regression towards the mean, etc don't play explain any grp diffs btwn parent income and child GCA, but this alone explains most of what we see.
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You can do the regression in NLSYs I think.
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Yeah, but I wanted simulated data for higher n and so I can assume away issues with measurement error etc. I've done this sort of exercise with data like NLSY before though w/ similar results (albeit somewhat noisier)
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as in, given the modest *individual* income-GCA correlation & well-established diffs in GCA distributions, the parents themselves can be expected to have markedly different GCA conditional on income (don't need msrmnt error, RTM, etc to explain presence of sizable cond'l gap)
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(RE: gaps in child test scores conditional on parent income)
End of conversation
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